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Data-driven optimal decomposition of time series

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  • Heiler, Siegfried
  • Feng, Yuanhua

Abstract

A data-driven optimal decomposition of time series with trend-cyclical and seasonal components as well as the estimation of derivatives of the trend-cyclical is considered. The time series is smoothed by locally weighted regression with polynomials and trigonometric functions as local regressors. Two variates for the selection of the optimal bandwidths and the order of the polynomials are proposed with a particular approach for the estimation in the boundary areas of the time series. The second of these procedures can also be used for the selection of optimal bandwidths if only one component is considered. The smoothing of a time series without seasonal variations is just a special case for these procedures. The rate of convergence in the second procedure for this special case is discussed. A by-product of this work is the development of a seasonal-difference-based method to estimate the variance in a seasonal time series.

Suggested Citation

  • Heiler, Siegfried & Feng, Yuanhua, 1995. "Data-driven optimal decomposition of time series," Discussion Papers, Series II 287, University of Konstanz, Collaborative Research Centre (SFB) 178 "Internationalization of the Economy".
    • Handle: RePEc:zbw:kondp2:287
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    References listed on IDEAS

    as
    1. Heiler, Siegfried & Feng, Yuanhua, 1995. "A simple root n bandwidth selector for nonparametric regression," Discussion Papers, Series II 286, University of Konstanz, Collaborative Research Centre (SFB) 178 "Internationalization of the Economy".
    2. Cleveland, William S. & Devlin, Susan J. & Grosse, Eric, 1988. "Regression by local fitting : Methods, properties, and computational algorithms," Journal of Econometrics, Elsevier, vol. 37(1), pages 87-114, January.
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    Cited by:

    1. Beran, Jan & Heiler, Mark A., 2008. "A nonparametric regression cross spectrum for multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 99(4), pages 684-714, April.
    2. Heiler, Siegfried & Feng, Yuanhua, 1995. "A simple root n bandwidth selector for nonparametric regression," Discussion Papers, Series II 286, University of Konstanz, Collaborative Research Centre (SFB) 178 "Internationalization of the Economy".
    3. Yuanhua Feng, 2013. "An iterative plug-in algorithm for decomposing seasonal time series using the Berlin Method," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(2), pages 266-281, February.

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